Resolution‐dependent behavior of subgrid‐scale vertical transport in the Zhang‐McFarlane convection parameterization. (18th April 2015) - Xiao, Heng; Gustafson, William I.; Hagos, Samson M.; Wu, Chien‐Ming; Wan, Hui
Abstract To better understand the behavior of quasi‐equilibrium‐based convection parameterizations at higher resolution, we use a diagnostic framework to examine the resolution‐dependence of subgrid‐scale vertical transport of moist static energy as parameterized by the Zhang‐McFarlane convection parameterization (ZM). Grid‐scale input to ZM is supplied by coarsening output from cloud‐resolving model (CRM) simulations onto subdomains ranging in size from 8 × 8 to 256 × 256 km2. Then the ZM‐based parameterization of vertical transport of moist static energy for scales smaller than the subdomain size ( <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj22d9t5gz" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />w′h′¯ZM</alternatives>) are compared to those directly calculated from the CRM simulations ( <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj22d9t5j2" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />w′h′¯CRM</alternatives>) for different subdomain sizes. The ensemble mean <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj22d9t5dv" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />w′h′¯CRM</alternatives> decreases by more than half as the subdomain size decreases from 128 to 8 km across while <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj22d9t5fd" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />w′h′¯ZM</alternatives> decreases with subdomain size only for strong convection cases and increases for weaker cases. The resolution dependence of <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj22d9t5rc" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />w′h′¯ZM</alternatives> is determined by the positive‐definite grid‐scale tendency of convective available potential energy (CAPE) in the convective quasi‐equilibrium (QE) closure. Further analysis shows the actual grid‐scale tendency of CAPE (before taking the positive definite value) and <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj22d9t5v1" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />w′h′¯CRM</alternatives> behave very similarly as the subdomain size changes because they are both tied to grid‐scale advective tendencies. We can improve the resolution dependence of <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj22d9t5nq" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />w′h′¯ZM</alternatives> significantly by averaging the grid‐scale tendency of CAPE over an appropriately large area surrounding each subdomain before taking its positive definite value. Even though the ensemble mean <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj22d9t5qt" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />w′h′¯CRM</alternatives> decreases with increasing resolution, its variability increases dramatically. <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgj22d9t51s" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />w′h′¯ZM</alternatives> cannot capture such increase in the variability, suggesting the need for stochastic treatment of convection at relatively high spatial resolution (8 or 16 km).